List of Errors in Free Lattices
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- Page 7, line 6
- Change lattice to lattices
- Page 11, proof of Lemma 1.3
- (Margarita Ramalho) Zorn's lemma should be invoked here. But a
direct proof avoiding Choice is not difficult.
- Page 8, line 28
- "An element in a lattice."
- Page 18, line 22
- Change "are" to "exists."
- Page 71, line 12
- The statement about \( J(p) \) should read:
\( J(p) \) is the smallest set such that every join cover of
an element in
\( J(p) \) can be refined to one in
\( J(p) \).
- Page 98, line 38
- In the proof of Lemma 5.6 replace
that begins "First consider the case ...", with
First note that if \(a \sqsubseteq c\) and \(b \sqsubseteq c\),
then, since \(c \in A(a) \cap B(b)\), the special property of \(\sqsubseteq\)
gives \(a \sim c \sim b\).
Now consider the case when \(a \sqsubseteq b\).
If \(b \sqsubseteq c\), then by the above remarks \(a \sim c \sim b\).
This implies \(g(a)\) is a joinand of \(g(b)\), and so \(g(a) \le g(b)\). Hence
we may assume \(c \sqsubset b\), and thus
by induction \(g(a) \le g(c)\). Also \(g(c)\) is a joinand of \(g(b)\) and so
\(g(c) \le g(b)\) and hence \(g(a) \le g(b)\).
- Page 99, line 29
- Change \(\ll\) to \(\leq\)
- Page 100, line 16
- The reference to Theorem 2.14 should be to Corollary 2.16.
- Page 141, Corollary 6.12
- Change both occurances of \(\sigma\) to \(\tau\) in this corollary since
\(\sigma\) is used for a certain endomorphism of FL(X) in
this chapter. Also change the \(\sigma\) on the subscript of y in
line 10 to \(\tau\) but leave the three \(\sigma\)'s in the displayed formula
- Page 212, line (3) of the listing
- Change P to S.
- Page 217, line (7) of the listing
- Remove the statement \(T\gets\emptyset\) and place it in between
lines (8) and (9) (and renumber the lines).
- Page 217, line (14) of the listing
- Change the \(\lt\) to \(\gt\).
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